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### 26.2 Statistics on Sliding Windows of Data

It is often useful to calculate descriptive statistics over a subsection (i.e., window) of a full dataset. Octave provides the function `movfun` which will call an arbitrary function handle with windows of data and accumulate the results. Many of the most commonly desired functions, such as the moving average over a window of data (`movmean`), are already provided.

: y = movfun (fcn, x, wlen) ¶
: y = movfun (fcn, x, [nb, na]) ¶
: y = movfun (…, "property", value) ¶

  Apply function fcn to a moving window of length wlen on data x.

  If wlen is a scalar, the function fcn is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movfun` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movfun` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  During calculations the data input x is reshaped into a 2-dimensional wlen-by-N matrix and fcn is called on this new matrix. Therefore, fcn must accept an array input argument and apply the computation along dimension 1, i.e., down the columns of the array.

  When applied to an array (possibly multi-dimensional) with n columns, fcn may return a result in either of two formats: Format 1) an array of size 1-by-n-by-dim3-by-…-by-dimN. This is the typical output format from Octave core functions. Type `demo ("movfun", 5)` for an example of this use case. Format 2) a row vector of length `n * numel_higher_dims` where numel_higher_dims is `prod (size (x)(3:end))`. The output of fcn for the i-th input column must be found in the output at indices `i:n:(n*numel_higher_dims)`. This format is useful when concatenating functions into arrays, or when using `nthargout`. Type `demo ("movfun", 6)` for an example of this case.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"dim"`

    Operate along the dimension specified, rather than the default of the first non-singleton dimension.

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = fcn (x(1:2))`, and `y(end) = fcn (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = fcn ([NaN, x(1:2)])`, and `y(end) = fcn ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how fcn handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = fcn ([user_value, x(1:2)])`, and `y(end) = fcn ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = fcn ([x(1), x(1:2)])`, and `y(end) = fcn ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = fcn ([x(end), x(1:2)])`, and `y(end) = fcn ([x(end-1:end), x(1)])`.

    Note that for some of these choices, the window size at the boundaries is not the same as for the central part, and fcn must work in these cases.

  `"nancond"`

    Controls whether `NaN` and `NA` values should be included (value: `"includenan"`), or excluded (value: `"omitnan"`), from the data passed to fcn. The default is `"includenan"`. Caution: The `"omitnan"` option is not yet implemented.

  `"outdim"`

    A row vector that selects which dimensions of the calculation will appear in the output y. This is only useful when fcn returns an N-dimensional array in Format 1. The default is to return all output dimensions.

  Programming Note: The property `"outdim"` can be used to save memory when the output of fcn has many dimensions, or when a wrapper to the base function that selects the desired outputs is too costly. When memory is not an issue, the easiest way to select output dimensions is to first calculate the complete result with `movfun` and then filter that result with indexing. If code complexity is not an issue then a wrapper can be created using anonymous functions. For example, if `basefcn` is a function returning a K-dimensional row output, and only dimension D is desired, then the following wrapper could be used.

      fcn = @(x) basefcn (x)(:,columns(x) * (D-1) + (1:columns(x)));
      y = movfun (@fcn, …);

  See also: movslice, prepad, postpad, permute, reshape.

: slcidx = movslice (N, wlen) ¶
: [slcidx, C, Cpre, Cpost, win] = movslice (…) ¶

  Generate indices to slice a vector of length N into windows of length wlen.

  The input N must be a positive integer.

  The moving window length input wlen can either be a scalar not equal to 1 or a 2-element array of integers. For scalar values, if odd the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. If wlen is even the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. When wlenis a 2-element array , `[nb, na]`, the window includes nb elements to the left of the current element and na elements to the right of the current element.

  The output slcidx is an array of indices of the slices that fit fully within the vector, where each column is an individual slice as the window moves from left to right. The slices have wlen elements for scalar wlen, or `nb + na + 1` elements for array valued wlen.

  Optional output C is an row vector of window center positions where the window stays fully within the vector.

  Optional outputs Cpre and Cpost contain the vector elements at the start and end of the vector, respectively, that result in the window extending beyond the ends of the vector.

  Optional output win is a column vector with the same number of rows as slcidx that contains the moving window defined as a center relative position stencil.

  See also: movfun.

: y = movmad (x, wlen) ¶
: y = movmad (x, [nb, na]) ¶
: y = movmad (…, dim) ¶
: y = movmad (…, "nancond") ¶
: y = movmad (…, property, value) ¶

  Calculate the moving mean absolute deviation over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `mad` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movmad` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movmad` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  If the optional argument dim is given, operate along this dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `mad`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = mad (x(1:2))`, and `y(end) = mad (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = mad ([NaN, x(1:2)])`, and `y(end) = mad ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `mad` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = mad ([user_value, x(1:2)])`, and `y(end) = mad ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = mad ([x(1), x(1:2)])`, and `y(end) = mad ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = mad ([x(end), x(1:2)])`, and `y(end) = mad ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmax, movmean, movmedian, movmin, movprod, movstd, movsum, movvar.

: y = movmax (x, wlen) ¶
: y = movmax (x, [nb, na]) ¶
: y = movmax (…, dim) ¶
: y = movmax (…, "nancond") ¶
: y = movmax (…, property, value) ¶

  Calculate the moving maximum over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `max` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movmax` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movmax` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  If the optional argument dim is given, operate along this dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `max`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = max (x(1:2))`, and `y(end) = max (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = max ([NaN, x(1:2)])`, and `y(end) = max ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `max` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = max ([user_value, x(1:2)])`, and `y(end) = max ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = max ([x(1), x(1:2)])`, and `y(end) = max ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = max ([x(end), x(1:2)])`, and `y(end) = max ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmean, movmedian, movmin, movprod, movstd, movsum, movvar.

: y = movmean (x, wlen) ¶
: y = movmean (x, [nb, na]) ¶
: y = movmean (…, dim) ¶
: y = movmean (…, "nancond") ¶
: y = movmean (…, property, value) ¶

  Calculate the moving average over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `mean` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movmean` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movmean` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  If the optional argument dim is given, operate along this dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `mean`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = mean (x(1:2))`, and `y(end) = mean (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = mean ([NaN, x(1:2)])`, and `y(end) = mean ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `mean` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = mean ([user_value, x(1:2)])`, and `y(end) = mean ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = mean ([x(1), x(1:2)])`, and `y(end) = mean ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = mean ([x(end), x(1:2)])`, and `y(end) = mean ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmax, movmedian, movmin, movprod, movstd, movsum, movvar.

: y = movmedian (x, wlen) ¶
: y = movmedian (x, [nb, na]) ¶
: y = movmedian (…, dim) ¶
: y = movmedian (…, "nancond") ¶
: y = movmedian (…, property, value) ¶

  Calculate the moving median over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `movmedian` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movmedian` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movmedian` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  If the optional argument dim is given, operate along this dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `movmedian`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = movmedian (x(1:2))`, and `y(end) = movmedian (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = movmedian ([NaN, x(1:2)])`, and `y(end) = movmedian ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `movmedian` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = movmedian ([user_value, x(1:2)])`, and `y(end) = movmedian ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = movmedian ([x(1), x(1:2)])`, and `y(end) = movmedian ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = movmedian ([x(end), x(1:2)])`, and `y(end) = movmedian ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmax, movmean, movmin, movprod, movstd, movsum, movvar.

: y = movmin (x, wlen) ¶
: y = movmin (x, [nb, na]) ¶
: y = movmin (…, dim) ¶
: y = movmin (…, "nancond") ¶
: y = movmin (…, property, value) ¶

  Calculate the moving minimum over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `min` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movmin` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movmin` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  If the optional argument dim is given, operate along this dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `min`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = min (x(1:2))`, and `y(end) = min (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = min ([NaN, x(1:2)])`, and `y(end) = min ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `min` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = min ([user_value, x(1:2)])`, and `y(end) = min ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = min ([x(1), x(1:2)])`, and `y(end) = min ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = min ([x(end), x(1:2)])`, and `y(end) = min ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmax, movmean, movmedian, movprod, movstd, movsum, movvar.

: y = movprod (x, wlen) ¶
: y = movprod (x, [nb, na]) ¶
: y = movprod (…, dim) ¶
: y = movprod (…, "nancond") ¶
: y = movprod (…, property, value) ¶

  Calculate the moving product over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `movprod` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movprod` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movprod` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  If the optional argument dim is given, operate along this dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `movprod`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = movprod (x(1:2))`, and `y(end) = movprod (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = movprod ([NaN, x(1:2)])`, and `y(end) = movprod ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `movprod` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = movprod ([user_value, x(1:2)])`, and `y(end) = movprod ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = movprod ([x(1), x(1:2)])`, and `y(end) = movprod ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = movprod ([x(end), x(1:2)])`, and `y(end) = movprod ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movstd, movsum, movvar.

: y = movstd (x, wlen) ¶
: y = movstd (x, [nb, na]) ¶
: y = movstd (…, opt) ¶
: y = movstd (…, opt, dim) ¶
: y = movstd (…, "nancond") ¶
: y = movstd (…, property, value) ¶

  Calculate the moving standard deviation over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `movstd` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movstd` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movstd` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  The optional argument opt determines the type of normalization to use. Valid values are

  0:

    normalize with N-1, provides the square root of the best unbiased estimator of the variance [default]

  1:

    normalize with N, this provides the square root of the second moment around the mean

  If the optional argument dim is given, operate along this dimension. The normalization argument opt must be given before the dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `movstd`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = movstd (x(1:2))`, and `y(end) = movstd (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = movstd ([NaN, x(1:2)])`, and `y(end) = movstd ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `movstd` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = movstd ([user_value, x(1:2)])`, and `y(end) = movstd ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = movstd ([x(1), x(1:2)])`, and `y(end) = movstd ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = movstd ([x(end), x(1:2)])`, and `y(end) = movstd ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movprod, movsum, movvar.

: y = movsum (x, wlen) ¶
: y = movsum (x, [nb, na]) ¶
: y = movsum (…, dim) ¶
: y = movsum (…, "nancond") ¶
: y = movsum (…, property, value) ¶

  Calculate the moving sum over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `movsum` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movsum` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movsum` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  If the optional argument dim is given, operate along this dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `movsum`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = movsum (x(1:2))`, and `y(end) = movsum (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = movsum ([NaN, x(1:2)])`, and `y(end) = movsum ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `movsum` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = movsum ([user_value, x(1:2)])`, and `y(end) = movsum ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = movsum ([x(1), x(1:2)])`, and `y(end) = movsum ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = movsum ([x(end), x(1:2)])`, and `y(end) = movsum ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movprod, movstd, movvar.

: y = movvar (x, wlen) ¶
: y = movvar (x, [nb, na]) ¶
: y = movvar (…, opt) ¶
: y = movvar (…, opt, dim) ¶
: y = movvar (…, "nancond") ¶
: y = movvar (…, property, value) ¶

  Calculate the moving variance over a sliding window of length wlen on data x.

  If wlen is a scalar, the function `var` is applied to a moving window of length wlen. When wlen is an odd number the window is symmetric and includes `(wlen - 1) / 2` elements on either side of the central element. For example, when calculating the output at index 5 with a window length of 3, `movvar` uses data elements `[4, 5, 6]`. If wlen is an even number, the window is asymmetric and has `wlen/2` elements to the left of the central element and `wlen/2 - 1` elements to the right of the central element. For example, when calculating the output at index 5 with a window length of 4, `movvar` uses data elements `[3, 4, 5, 6]`.

  If wlen is an array with two elements `[nb, na]`, the function is applied to a moving window `-nb:na`. This window includes nb number of elements before the current element and na number of elements after the current element. The current element is always included. For example, given `wlen = [3, 0]`, the data used to calculate index 5 is `[2, 3, 4, 5]`.

  The optional argument opt determines the type of normalization to use. Valid values are

  0:

    normalize with N-1, provides the best unbiased estimator of the variance [default]

  1:

    normalizes with N, this provides the second moment around the mean

  If the optional argument dim is given, operate along this dimension. The normalization argument opt must be given before the dimension.

  The optional string argument `"nancond"` controls whether `NaN` and `NA` values should be included (`"includenan"`), or excluded (`"omitnan"`), from the data passed to `var`. The default is `"includenan"`. Caution: the `"omitnan"` option is not yet implemented.

  The calculation can be controlled by specifying property/value pairs. Valid properties are

  `"Endpoints"`

    This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:

    `"shrink"` (default)

      The window is truncated at the beginning and end of the array to exclude elements for which there is no source data. For example, with a window of length 3, `y(1) = var (x(1:2))`, and `y(end) = var (x(end-1:end))`.

    `"discard"`

      Any y values that use a window extending beyond the original data array are deleted. For example, with a 10-element data vector and a window of length 3, the output will contain only 8 elements. The first element would require calculating the function over indices `[0, 1, 2]` and is therefore discarded. The last element would require calculating the function over indices `[9, 10, 11]` and is therefore discarded.

    `"fill"`

      Any window elements outside the data array are replaced by `NaN`. For example, with a window of length 3, `y(1) = var ([NaN, x(1:2)])`, and `y(end) = var ([x(end-1:end), NaN])`. This option usually results in y having `NaN` values at the boundaries, although it is influenced by how `var` handles `NaN`, and also by the property `"nancond"`.

    user_value

      Any window elements outside the data array are replaced by the specified value user_value which must be a numeric scalar. For example, with a window of length 3, `y(1) = var ([user_value, x(1:2)])`, and `y(end) = var ([x(end-1:end), user_value])`. A common choice for user_value is 0.

    `"same"`

      Any window elements outside the data array are replaced by the value of x at the boundary. For example, with a window of length 3, `y(1) = var ([x(1), x(1:2)])`, and `y(end) = var ([x(end-1:end), x(end)])`.

    `"periodic"`

      The window is wrapped so that any missing data elements are taken from the other side of the data. For example, with a window of length 3, `y(1) = var ([x(end), x(1:2)])`, and `y(end) = var ([x(end-1:end), x(1)])`.

  `"SamplePoints"`

    Caution: This option is not yet implemented.

  Programming Note: This function is a wrapper which calls `movfun`. For additional options and documentation, see `movfun`.

  See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movprod, movstd, movsum.

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